Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

doi:10.1088/1674-1056/ad7afb

Abstract This paper delves into the dynamical analysis, chaos control, Mittag-Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0-1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

Keywords: FOFR system dynamical analysis control boundedness forecasting

Received: 06 July 2024
Revised: 06 September 2024
Accepted manuscript online: 14 September 2024

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Jn	(High-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project jointly supported by the National Natural Science Foundation of China (Grant No. 12372013), Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 24HASTIT034), the Natural Science Foundation of Henan Province, China (Grant No. 232300420122), the Humanities and Society Science Foundation from the Ministry of Education of China (Grant No. 19YJCZH265), China Postdoctoral Science Foundation (Grant No. 2019M651633), First Class Discipline of Zhejiang-A (Zhejiang University of Finance and EconomicsStatistics), the Collaborative Innovation Center for Data Science and Big Data Analysis (Zhejiang University of Finance and Economics-Statistics).

Corresponding Authors: Song Zheng
E-mail: szh070318@zufe.edu.cn

Cite this article:

Kehao Yang(杨轲皓), Song Zheng(郑松), Tianhu Yu(余天虎), Aceng Sambas, Muhamad Deni Johansyah, Hassan Saberi-Nik, and Mohamad Afendee Mohamed Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system 2024 Chin. Phys. B 33 110501

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Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

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